American academic Raymond M. Smullyan was famous not only for his math research but also for the multitude of books he wrote full of paradoxes and riddles.

### A portrait

### A strange verdict

### Family connections

### The elevator

### Coins

### The Catholic

### The snail

And now for some slightly more difficult riddles.

### How much are the birds?

### Profit

### A bear’s fur

### The tree puzzle

An evil king imprisons 2 people, Alice and Bob. They are placed in the king’s evil castle in separate towers. Each tower has a window. Through the windows, Alice and Bob can see separate parts of the castle’s garden. In the garden, 20 trees grow. The prisoners can’t communicate in any way with each other.

Alice can see 12 trees through the window in tower A.

Bob can see 8 trees through the window in tower B.

Both are told that the garden has either 18 or 20 trees, that together they see all the trees, and that no tree is seen by both of them.

Every day, starting with the day they are imprisoned, a guard asks them a question. The guard first asks Alice. If no answer is given, he goes on to ask Bob. The question asked is: “Are there 18 or 20 trees in the garden?”

If the prisoner answers correctly, both prisoners are released immediately.

If the prisoner answers erroneously, both prisoners are executed immediately.

The prisoner can choose not to answer, in which case the guard will continue to ask the next prisoner as mentioned above. (The prisoner will choose this if they are not sure since we assume both prisoners to be completely logical entities.)

Will the prisoners ever be released? After how many days?